A partition of a number $n \in \mathbb N$ as a sum of positive integers that add up to $n$. The order of components in the sum does not matter.
Let $A$ be the number of partitions of $n$ into 4 parts.
Let $B$ be the number of partitions of $3n$ into 4 parts each of which is not greater than $n-1$.
Prove that $A=B$.
Consider the bijection $A \rightarrow B$: $$\{a,b,c,d\} \rightarrow \{n-a,n-b,n-c,n-d\}$$
since $a+b+c+d = n$ and $n > a,b,c,d \geq 1$ you get that $$(n-a)+(n-b)+(n-c)+(n-d) = 4n-n =3n$$ and that $ n-1 \geq n-a,n-b,n-c,n-d$